Effect of different jump distributions on the dynamics of jump processes
Abstract
The paper investigates stochastic processes forced by independent and identically
distributed jumps occurring according to a Poisson process. The impact of different
distributions of the jump amplitudes are analyzed for processes with linear drift.
Exact expressions of the probability density functions are derived when jump amplitudes
are distributed as exponential, gamma, and mixture of exponential distributions for
both natural and reflecting boundary conditions. The mean level-crossing properties
are studied in relation to the different jump amplitudes. As an example of application
of the previous theoretical derivations, the role of different rainfall-depth distributions
on an existing stochastic soil water balance model is analyzed. It is shown how the
shape of distribution of daily rainfall depths plays a more relevant role on the soil
moisture probability distribution as the rainfall frequency decreases, as predicted
by future climatic scenarios. © 2010 The American Physical Society.
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https://hdl.handle.net/10161/4288Published Version (Please cite this version)
10.1103/PhysRevE.81.061133Publication Info
Daly, Edoardo; & Porporato, Amilcare (2010). Effect of different jump distributions on the dynamics of jump processes. Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, 81(6). pp. 61133. 10.1103/PhysRevE.81.061133. Retrieved from https://hdl.handle.net/10161/4288.This is constructed from limited available data and may be imprecise. To cite this
article, please review & use the official citation provided by the journal.
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Show full item recordScholars@Duke
Amilcare Porporato
Adjunct Professor in the Department of Civil and Environmental Engineering
Amilcare Porporato earned a Master Degree in Civil Engineering (summa cum laude) in
1992 and his Ph.D. in 1996 from Polytechnic of Turin. He was appointed Assistant Professor
in the Department of Hydraulics of the Polytechnic of Turin, and he moved to Duke
University in 2003, where he is now Full Professor in the Department of Civil and
Environmental Engineering with a secondary appointment with the Nicholas School of
the Environment.
In June 1996, Porporato received the Arturo Parisatti

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